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Question
Math
Posted 2 months ago

ABundefined\overleftrightarrow{A B} and CDundefined\overleftrightarrow{C D} are parallel lines

Which translation of the plane can we use to prove angles xx and yy are congruent, and why?

Choose 1 answer:
(A) A translation along the directed line segment CBC B maps line CDundefined\overleftrightarrow{C D} onto line ABundefined\overleftrightarrow{A B} and angle yy onto angle xx.
(B) A translation along the directed line segment ACA C maps line ABundefined\overleftrightarrow{A B} onto line CDundefined\overleftrightarrow{C D} and angle xx onto angle yy.
C) A translation along the directed line segment ABA B maps line CDundefined\overleftrightarrow{C D} onto line ABundefined\overleftrightarrow{A B} and angle yy onto angle xx
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 2
Corresponding angles are congruent if the lines are parallel and they are cut by a transversal
step 3
A translation is a transformation that slides every point of a figure the same distance in the same direction
step 4
To prove angles xx and yy are congruent using translation, we need to slide line CDundefined \overleftrightarrow{CD} onto line ABundefined \overleftrightarrow{AB} such that angle yy coincides with angle xx
step 5
The translation along the directed line segment CBCB will map line CDundefined \overleftrightarrow{CD} onto line ABundefined \overleftrightarrow{AB} and angle yy onto angle xx
A
Key Concept
Translations and Corresponding Angles
Explanation
When parallel lines are cut by a transversal, corresponding angles are congruent. A translation that maps one line onto another and one angle onto another can be used to prove the congruence of those angles.

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